cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A256388 Numbers n such that a single prime is the arithmetic mean of 2 semiprimes whose difference is 2*n.

Original entry on oeis.org

1, 3, 9, 15, 27, 39, 57, 69, 99, 105, 135, 147, 177, 189, 195, 225, 237, 267, 279, 309, 345, 417, 429, 459, 519, 567, 597, 615, 639, 657, 807, 819, 825, 855, 879, 1017, 1029, 1047, 1059, 1089, 1149, 1227, 1275, 1287, 1299, 1317, 1425, 1449, 1479, 1485, 1605
Offset: 1

Views

Author

Michel Marcus, Mar 27 2015

Keywords

Comments

That is, there is a single prime p, such that p+n and p-n are both semiprime.
Subsequence of A256389.

Examples

			A256381 is the list of numbers n such that n-3 and n+3 are semiprimes, and it contains a single prime, hence 3 is in the sequence.

Crossrefs

Cf. A124936, A256381.
Cf. A256387 (no prime), A256389 (one or more primes).

Formula

Conjecture: a(n) = A001359(n)-2. - Benedict W. J. Irwin, Apr 26 2016

A256382 Numbers n such that n-4 and n+4 are semiprimes.

Original entry on oeis.org

10, 18, 29, 30, 42, 53, 61, 73, 78, 81, 89, 90, 91, 115, 119, 125, 137, 138, 162, 165, 173, 181, 198, 205, 209, 210, 213, 217, 222, 258, 263, 291, 295, 299, 305, 323, 325, 330, 331, 390, 399, 407, 411, 441, 449, 450, 462, 477, 485, 489, 493, 497, 501, 515, 523
Offset: 1

Views

Author

Michel Marcus, Mar 27 2015

Keywords

Comments

A117328 is the subsequence of primes.

Links

Crossrefs

Cf. A001358 (semiprimes).
Cf. A117328 (with primes rather than semiprimes).
Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).
Cf. A256381 (n-3 and n+3), A256383 (n-5 and n+5).

Programs

  • Magma
    IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [6..750] | IsSemiprime(n+4) and IsSemiprime(n-4) ]; // Vincenzo Librandi, Mar 29 2015
  • Mathematica
    Select[Range[600], PrimeOmega[# + 4] == PrimeOmega[# - 4] == 2 &] (* Vincenzo Librandi, Mar 29 2015 *)
Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,600}],9,1],?(#[[1]]==#[[9]]==1&),{1},Heads->False]]+4 (* _Harvey P. Dale, Mar 29 2015 *)
  • PARI
    lista(nn,m=4) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}

A256383 Numbers n such that n-5 and n+5 are semiprimes.

Original entry on oeis.org

9, 20, 30, 44, 60, 82, 90, 116, 124, 128, 138, 150, 164, 182, 208, 210, 214, 242, 254, 294, 296, 300, 304, 314, 324, 334, 360, 366, 376, 386, 398, 408, 412, 422, 432, 442, 476, 506, 510, 522, 524, 532, 538, 540, 548, 578, 584, 586, 628, 674, 676, 684
Offset: 1

Views

Author

Michel Marcus, Mar 27 2015

Keywords

Comments

It appears that there are no primes in this sequence.
If n is odd, one of n+5 and n-5 is divisible by 4, so unless n = 9 it can't be a semiprime. Thus all terms except 9 are even. - Robert Israel, Apr 13 2020

Links

Crossrefs

Cf. A001358 (semiprimes).
Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).
Cf. A256381 (n-3 and n+3), A256382 (n-4 and n+4).

Programs

  • Magma
    IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [6..700] | IsSemiprime(n+5) and IsSemiprime(n-5) ]; // Vincenzo Librandi, Mar 29 2015
  • Maple
    N:= 1000: # for terms <= N-5
PP:= select(isprime, {seq(i,i=3..N/3,2)}):
P:= select(`<=`,PP,floor(sqrt(N))):
SP:= {}:
for p in P do
  PP:= select(`<=`,PP,N/p);
  SP:= SP union map(`*`,PP,p);
od:
R:= {9} union (map(`+`,SP,5) intersect map(`-`,SP,5)):
sort(convert(R,list)); # Robert Israel, Apr 13 2020
  • Mathematica
    Select[Range[2, 700], PrimeOmega[# + 5] == PrimeOmega[# - 5] == 2 &] (* Vincenzo Librandi, Mar 29 2015 *)
  • PARI
    lista(nn,m=5) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}
  • PARI
    issemi(n)=bigomega(n)==2
list(lim)=my(v=List([9])); forprime(p=5,(lim-5)\3, if(issemi(3*p+10), listput(v,3*p+5))); forprime(p=29,(lim+5)\3, if(issemi(3*p-10), listput(v,3*p-5))); forstep(n=30,lim\=1,6, if(issemi(n-5) && issemi(n+5), listput(v, n))); Set(v) \\ Charles R Greathouse IV, Apr 13 2020

A256389 Numbers n such that one or more primes can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 46, 48, 50, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 69, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110
Offset: 1

Views

Author

Michel Marcus, Mar 27 2015

Keywords

Comments

That is, there are several primes p, such that p+n and p-n are both semiprime.
Complement of A256387.
The terms of this sequence that do not belong to A256388 are even.

Examples

			A256381 is the list of numbers n such that n-3 and n+3 are semiprimes, and it contains a single prime, hence 3 is in the sequence.
A256382 is the list of numbers n such that n-4 and n+4 are semiprimes, and it contains several primes, hence 4 is in the sequence.

Crossrefs

Cf. A124936, A105571, A256382.
Cf. A256387 (no prime), A256388 (a single prime).
Showing 1-4 of 4 results.

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